Light scattering detectors and methods for the same

ABSTRACT

Methods for determining a radius of gyration of a particle in solution using a light scattering detector are provided. The method may include passing the solution through a flowpath in a sample cell, determining respective angular normalization factors for first and second angles of the detector, obtaining a first scattering intensity of the particle in solution at the first angle, obtaining a second scattering intensity of the particle in solution at the second angle, obtaining a 10° scattering intensity of the particle in solution at an angle of about 10°, determining a first particle scattering factor, determining a second particle scattering factor, plotting an angular dissymmetry plot, fitting a line to the angular dissymmetry plot, determining a slope of the line at a selected location on the line, determining the radius of gyration of the particle in solution from the slope of the line, and outputting the radius of gyration.

BACKGROUND

Conventional light scattering detectors are often utilized inconjunction with chromatographic techniques to determine one or morephysical attributes or characteristics of various molecules or solutessuspended in solutions. For example, light scattering detectors areoften utilized with gel permeation chromatography (GPC) to determine amolecular weight and a radius of gyration of various particles, such aspolymers. In light scattering detectors, a sample or effluent containingmolecules (e.g., polymers) is flowed through a sample cell from an inletto an outlet disposed at opposing ends thereof. As the effluent isflowed through the sample cell, the effluent is illuminated by acollimated beam of light (e.g., laser). The interaction of the beam oflight and the polymers of the effluent produces scattered light. Thescattered light is then measured and analyzed for varying attributes,such as intensity and angle, to determine the physical characteristicsof the polymers.

While conventional light scattering detectors have proven to beeffective for determining the physical attributes of a wide variety ofmolecules, conventional light scattering detectors are limited in theirability to analyze small molecules. For example, conventional lightscattering detectors often lack the sensitivity and/or resolution tomeasure Rg of molecules having a radius of gyration of less than about10 nm. In view of the foregoing, conventional light scattering detectorsoften incorporate lasers having relatively greater power or energy toincrease the sensitivity of the detectors. Incorporating lasers withgreater power, however, is cost prohibitive and often requires largerinstruments due to the relatively larger footprint of the lasers.Alternatively, the volume of the sample cells in conventional lightscattering detectors can been increased to increase the intensity ofscattered light. Increasing the volume of conventional sample cells,however, leads to excessive peak broadening.

What is needed, then, are improved light scattering detectors and samplecells thereof, methods for increasing the sensitivity and/or resolutionof the light scattering detectors without increasing peak broadening,and improved methods for determining a radius of gyration of a particle.

BRIEF SUMMARY

This summary is intended merely to introduce a simplified summary ofsome aspects of one or more implementations of the present disclosure.Further areas of applicability of the present disclosure will becomeapparent from the detailed description provided hereinafter. Thissummary is not an extensive overview, nor is it intended to identify keyor critical elements of the present teachings, nor to delineate thescope of the disclosure. Rather, its purpose is merely to present one ormore concepts in simplified form as a prelude to the detaileddescription below.

The foregoing and/or other aspects and utilities embodied in the presentdisclosure may be achieved by providing a method for determining aradius of gyration (Rg) of a particle in solution using a lightscattering detector. The method may include passing the particle insolution through a flowpath in a sample cell, wherein the flowpath has acenterline aligned with a beam of light of the detector. The method mayalso include determining an angular normalization factor (N_(θ1)) for afirst angle of the detector and an angular normalization factor (N_(θ2))of a second angle of the detector, wherein the first angle is about 90°relative to the centerline, and wherein the second angle is about 170°relative to the centerline. The method may also include obtaining afirst scattering intensity (I_(θ1)) of the particle in solution at thefirst angle. The method may also include obtaining a second scatteringintensity (I_(θ2)) of the particle in solution at the second angle. Themethod may also include obtaining a 10° scattering intensity (I₁₀) ofthe particle in solution at an angle of about 10°. The method may alsoinclude determining a first particle scattering factor (P_(θ1)) with thefirst scattering intensity (I_(θ1)), the 10° scattering intensity (I₁₀),and the angular normalization factor (N_(θ1)) for the first angle. Themethod may also include determining a second particle scattering factor(P_(θ2)) with the second scattering intensity (I_(θ2)), the 10°scattering intensity (I₁₀), and the angular normalization factor(N_(θ2)) for the second angle. The method may also include plotting anangular dissymmetry plot, wherein the angular dissymmetry plot comprisesthe first particle scattering factor (P_(θ1)) and the second particlescattering factor (P_(θ2)). The method may also include fitting a lineto the angular dissymmetry plot. The method may also include determininga slope of the line at a selected location on the line. The method mayalso include determining the radius of gyration (Rg) of the particle insolution from the slope of the line. The method may also includeoutputting the radius of gyration (Rg).

In at least one implementation, determining the angular normalizationfactor of the first and second angles of the detector may includepassing each of a plurality of known particles in solution through theflowpath of the sample cell. Determining the angular normalizationfactor of the first and second angles of the detector may also includeobtaining scattering intensity values for each of the plurality of knownparticles in solution at an angle of about 10°, at the first angle, andat the second angle. Determining the angular normalization factor of thefirst and second angles of the detector may also include determining theangular normalization factor (N_(θ1)) for the first angle with a plot ofa ratio of the scattering intensity values of each of the plurality ofknown particles at the first angle to the scattering intensity values ofeach of the plurality of known particles at an angle of about 10°.Determining the angular normalization factor of the first and secondangles of the detector may also include determining the angularnormalization factor (N_(θ2)) for the second angle with a plot of aratio of the scattering intensity values of each of the plurality ofknown particles at the second angle to the scattering intensity valuesof each of the plurality of known particles at an angle of about 10°.

In at least one implementation, each of the plurality of known particlesin solution have a known molecular weight.

In at least one implementation, the first particle scattering factor(P_(θ1)) is in the form

${P_{\theta 1} = \frac{\left( {I_{\theta \; 1}/I_{10}} \right)}{N_{\theta \; 1}}},$

where: I_(θ1) is the scattering intensity of the particle in solution atthe first angle; I₁₀ is the scattering intensity of the particle insolution at an angle of about 10°; and N_(θ1) is the angularnormalization factor for the first angle.

In at least one implementation, the second particle scattering factor(P_(θ2)) is in the form

${P_{\theta \; 2} = \frac{\left( {I_{\theta \; 2}/I_{10}} \right)}{N_{\theta \; 2}}},$

where: I_(θ2) is the scattering intensity of the particle in solution atthe second angle; I₁₀ is the scattering intensity of the particle insolution at an angle of about 10°; and N_(θ2) is the angularnormalization factor for the second angle.

In at least one implementation, plotting the angular dissymmetry plotcomprises: plotting a first point on a plane, the first point comprisinga first coordinate and a second coordinate, wherein the first coordinateof the first point is the first particle scattering factor (P_(θ1)), andwherein the second coordinate of the first point is in the form

${\mu_{\theta \; 1}^{2} = \left( \frac{4\pi \; n_{0}\sin \frac{\theta 1}{2}}{\lambda} \right)^{2}},$

where: n₀ is a refractive index of the solution; θ₁ is the first angle;and λ is a wavelength of the beam of light; plotting a second point onthe plane, the second point comprising a first coordinate and a secondcoordinate, wherein the first coordinate of the second point is thesecond particle scattering factor (P_(θ2)), and wherein the secondcoordinate of the second point is in the form

${\mu_{\theta_{2}}^{2} = \left( \frac{4\pi \; n_{0}\sin \frac{\theta_{2}}{2}}{\lambda} \right)^{2}},$

where: n₀ is a refractive index of the solution; θ₂ is the second angle;and λ is the wavelength of the beam of light.

In at least one implementation, fitting the line to the angulardissymmetry plot comprises a least squares fitting. The line may includea polynomial degree of less than three.

The foregoing and/or other aspects and utilities embodied in the presentdisclosure may be achieved by providing a method for determining aradius of gyration (Rg) of a particle in solution using a lightscattering detector. The method may include passing the particle insolution through a flowpath in a sample cell, wherein the flowpath has acenterline aligned with a beam of light of the detector. The method mayalso include determining an angular normalization factor (N_(θ1)) for afirst angle of the detector, wherein the first angle is either about 90°or about 170° relative to the centerline. The method may also includeobtaining a first scattering intensity (I_(θ1)) of the particle insolution at the first angle. The method may also include obtaining a 10°scattering intensity (I₁₀) of the particle in solution at an angle ofabout 10° or less. The method may also include determining a firstparticle scattering factor (P_(θ1)) with the first scattering intensity(I_(θ1)), the 10° scattering intensity (I₁₀), and the angularnormalization factor (N_(θ1)) for the first angle. The method may alsoinclude plotting an angular dissymmetry plot, wherein the angulardissymmetry plot comprises the first particle scattering factor(P_(θ1)). The method may also include fitting a line to the angulardissymmetry plot. The method may also include determining a slope of theline at a selected location on the line. The method may also includedetermining the radius of gyration (Rg) of the particle in solution fromthe slope of the line. The method may also include outputting the radiusof gyration.

In at least one implementation, determining the angular normalizationfactor (N_(θ1)) for the first angle of the detector comprises: passingeach of a plurality of known particles in solution through the flowpathof the sample cell; obtaining scattering intensity values of each of theplurality of known particles in solution at an angle of about 10° and atthe first angle; and determining the angular normalization factor(N_(θ1)) for the first angle with a plot of a ratio of the scatteringintensity values of each of the plurality of known particles at thefirst angle to the scattering intensity values of each of the pluralityof known particles at an angle of about 10° with respect to a respectiveweight average molecular weight of each of the plurality of knownparticles in solution.

In at least one implementation, each of the plurality of known particlesin solution have a known molecular weight.

In at least one implementation, the first particle scattering factor(P_(θ1)) is in the form

${P_{\theta_{1}} = \frac{\left( {I_{{\theta \;}_{1}}/I_{10}} \right)}{N_{\theta_{1}}}},$

where: I_(θ1) is the scattering intensity of the particle in solution atthe first angle; I₁₀ is the scattering intensity of the particle insolution at an angle of about 10°; and N_(θ1) is the angularnormalization factor for the first angle.

In at least one implementation, plotting the angular dissymmetry plotcomprises: plotting a first point on a plane, the first point comprisinga first coordinate and a second coordinate, wherein the first coordinateof the first point is the first particle scattering factor (P_(θ1)), andwherein the second coordinate of the first point is in the form

${\mu_{\theta_{1}}^{2} = \left( \frac{4\pi \; n_{0}\sin \frac{\theta_{1}}{2}}{\lambda} \right)^{2}},$

where: n₀ is a refractive index of the solution; θ₁ is the first angle;and λ is a wavelength of the beam of light.

In at least one implementation, the line of the angular dissymmetry plotis a straight line.

In at least one implementation, the radius of gyration (Rg) of theparticle in solution is less than 10 nm.

In at least one implementation, the method may further include:obtaining an angular normalization factor (N_(θ2)) of a second angle ofthe detector, wherein second angle is either about 90° or about 170°relative to the centerline, and wherein the second angle is differentfrom the first angle; obtaining a second scattering intensity (I_(θ2))of the particle in solution at the second angle; and determining asecond particle scattering factor (P_(θ2)) with the second scatteringintensity (I_(θ2)), the 10° scattering intensity (I₁₀), and the angularnormalization factor (N_(θ2)) for the second angle. The angulardissymmetry plot may further comprise the second particle scatteringfactor (P_(θ2)).

In at least one implementation, determining the angular normalizationfactor of the second angle of the detector comprises: obtainingscattering intensity values of each of the plurality of known particlesin solution at the second angle; and determining the angularnormalization factor (N_(θ2)) for the second angle with a plot of aratio of the scattering intensity values of each of the plurality ofknown particles at the second angle to the scattering intensity valuesof each of the plurality of known particles at an angle of about 10°with respect to a respective weight average molecular weight of each ofthe plurality of known particles in solution.

In at least one implementation, the second particle scattering factor(P_(θ2)) is in the form

${P_{\theta_{2}} = \frac{\left( {I_{\theta_{2}}/I_{10}} \right)}{N_{\theta_{2}}}},$

where: I_(θ2) is the scattering intensity of the particle in solution atthe second angle; I₁₀ is the scattering intensity of the particle insolution at an angle of about 10°; and N_(θ2) is the angularnormalization factor for the second angle.

In at least one implementation, plotting the angular dissymmetry plotfurther comprises: plotting a second point on the plane, the secondpoint comprising a first coordinate and a second coordinate, wherein thefirst coordinate of the second point is the second particle scatteringfactor (P_(θ2)), and wherein the second coordinate of the second pointis in the form

${\mu_{\theta_{2}}^{2} = \left( \frac{4\pi \; n_{0}\sin \frac{\theta_{2}}{2}}{\lambda} \right)^{2}},$

where: n₀ is a refractive index of the solution; θ₂ is the second angle;and A is the wavelength of the beam of light.

In at least one implementation, the line of the angular dissymmetry plotis a curved line.

In at least one implementation, the radius of gyration (Rg) of theparticle in solution is less than 100 nm, optionally greater than 10 nm.

Further areas of applicability of the present disclosure will becomeapparent from the detailed description provided hereinafter. It shouldbe understood that the detailed description and specific examples, whileindicating some typical aspects of the disclosure, are intended forpurposes of illustration only and are not intended to limit the scope ofthe disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate varying implementations of thepresent disclosure. These and/or other aspects and advantages in theimplementations of the disclosure will become apparent and more readilyappreciated from the following description of the variousimplementations, taken in conjunction with the accompanying drawings. Itshould be noted that some details of the drawings have been simplifiedand are drawn to facilitate understanding of the present disclosurerather than to maintain strict structural accuracy, detail, and scale.These drawings/figures are intended to be explanatory and notrestrictive.

FIG. 1A illustrates a schematic view of an exemplary light scatteringdetector including an exemplary sample cell, according to one or moreimplementations disclosed.

FIG. 1B illustrates a schematic view of the exemplary sample cell ofFIG. 1A, according to one or more implementations disclosed.

FIG. 1C illustrates the schematic view of the exemplary sample cell ofFIG. 1A without the analyte scattered light, according to one or moreimplementations disclosed.

FIG. 1D illustrates an enlarged view of the portion of the sample cellindicated by the box labeled 1D in FIG. 1C, according to one or moreimplementations disclosed.

FIG. 2 illustrates a plot of a ratio (I_(θ)/I₁₀) versus a respectiveweight average molecular weight of each of a plurality of knownparticles, according to one or more implementations disclosed.

FIG. 3 illustrates an angular dissymmetry plot, according to one or moreimplementations disclosed.

FIG. 4 illustrates an angular dissymmetry plot, according to one or moreimplementations disclosed.

FIG. 5 illustrates a computer system or electronic processor forreceiving and/or analyzing data from a light scattering detector,according to one or more implementations disclosed.

FIG. 6 illustrates a block diagram of the computer system or electronicprocessor of FIG. 5, according to one or more implementations disclosed.

DETAILED DESCRIPTION

The following description of various typical aspect(s) is merelyexemplary in nature and is in no way intended to limit the disclosure,its application, or uses.

As used throughout this disclosure, ranges are used as shorthand fordescribing each and every value that is within the range. It should beappreciated and understood that the description in a range format ismerely for convenience and brevity, and should not be construed as aninflexible limitation on the scope of any embodiments or implementationsdisclosed herein. Accordingly, the disclosed range should be construedto have specifically disclosed all the possible subranges as well asindividual numerical values within that range. As such, any value withinthe range may be selected as the terminus of the range. For example,description of a range such as from 1 to 5 should be considered to havespecifically disclosed subranges such as from 1.5 to 3, from 1 to 4.5,from 2 to 5, from 3.1 to 5, etc., as well as individual numbers withinthat range, for example, 1, 2, 3, 3.2, 4, 5, etc. This appliesregardless of the breadth of the range.

Additionally, all numerical values are “about” or “approximately” theindicated value, and take into account experimental error and variationsthat would be expected by a person having ordinary skill in the art. Itshould be appreciated that all numerical values and ranges disclosedherein are approximate values and ranges, whether “about” is used inconjunction therewith. It should also be appreciated that the term“about,” as used herein, in conjunction with a numeral refers to a valuethat may be ±0.01% (inclusive), ±0.1% (inclusive), ±0.5% (inclusive),±1% (inclusive) of that numeral, ±2% (inclusive) of that numeral, ±3%(inclusive) of that numeral, ±5% (inclusive) of that numeral, ±10%(inclusive) of that numeral, or ±15% (inclusive) of that numeral. Itshould further be appreciated that when a numerical range is disclosedherein, any numerical value falling within the range is alsospecifically disclosed.

All references cited herein are hereby incorporated by reference intheir entireties. In the event of a conflict in a definition in thepresent disclosure and that of a cited reference, the present disclosurecontrols.

As used herein, the term or expression “sensitivity” may refer to theratio of signal to noise. It should be appreciated by one havingordinary skill in the art that increasing laser power does notnecessarily improve the sensitivity.

FIG. 1A illustrates a schematic view of an exemplary light scatteringdetector (LSD) 100 including an exemplary sample cell 102, according toone or more implementations. The LSD 100 may be operably coupled with asample source or device 104, and capable of or configured to receive asample or effluent therefrom. For example, as illustrated in FIG. 1A,the LSD 100 may be fluidly coupled with the sample source or device 104via line 106 and configured to receive the effluent therefrom.Illustrative sample sources or devices 104 may include, but are notlimited to, a chromatography instrument capable of or configured toseparate one or more analytes of a sample or eluent from one another.For example, the sample source or device 104 may be a liquidchromatography instrument capable of or configured to separate theanalytes of the eluent from one another based on their respectivecharges (e.g., ion exchange chromatography), sizes (e.g., size-exclusionor gel permeation chromatography), or the like. In an exemplaryimplementation, the LSD 100 is operably coupled with a liquidchromatography instrument configured to separate the analytes from oneanother based on their respective sizes. For example, the LSD 100 isoperably coupled with a liquid chromatography instrument including gelpermeation chromatography columns.

The LSD 100 may include the exemplary sample cell 102, a collimated beamof light source, such as a laser 108, and one or more detectors 110,112, 114 (three are shown) operably coupled with one another. Thedetectors 110, 112, 114 may be any suitable detector capable of orconfigured to receive analyte scattered light. For example, any one ormore of the detectors 110, 112, 114 may be a photo-detector, such as asilicon photo-detector. The LSD 100 may include one or more lenses 116,118, 120, 122, 124 (five are shown) capable of or configured to refract,focus, attenuate, and/or collect light transmitted through the LSD 100,and one or more mirrors 126, 128 (two are shown) capable of orconfigured to reflect or redirect the light transmitted through the LSD100.

In at least one implementation, a first lens 116 and a second lens 118may be disposed on opposing sides or axial ends of the sample cell 102and configured to refract, focus, attenuate, and/or collect lighttransmitted therethrough. In another implementation, a body 130 of thesample cell 102 may define recesses 132, 134 configured to receive thefirst and second lenses 116, 118. For example, as illustrated in FIG. 1Aand further illustrated in detail in FIG. 1B, the body 130 of the samplecell 102 may define a first recess 132 and a second recess 134 extendinglongitudinally or axially therethrough, and configured to receive thefirst lens 116 and the second lens 118, respectively. As illustrated inFIGS. 1A and 1B, each of the first and second lenses 116, 118 may definea convex surface along respective first or outer end portions 136, 138thereof. While the first end portions 136, 138 of the first and secondlenses 116, 118 are illustrated as defining convex surfaces, it shouldbe appreciated that any one of the respective first end portions 136,138 of the first and second lenses 116, 118 may alternatively define aflat surface. As further illustrated in FIG. 1A, each of the first andsecond lenses 116, 118 may define a flat surface along respective secondor inner end portions 140, 142 thereof. As further described herein, therespective second end portions 140, 142 of the first and second lenses116, 118 may seal and/or at least partially define a channel or flowpath144 extending through the sample cell 102.

The laser 108 may be any suitable laser capable of or configured toprovide a beam of light 146 having sufficient wavelength and/or power.For example, the laser 108 may be a diode laser, a solid state laser, orthe like. The laser 108 may be configured to emit the beam of light 146through the sample cell 102. For example, as illustrated in FIG. 1A, thelaser 108 may be arranged or disposed about the LSD 100 such that thebeam of light 146 emitted therefrom is transmitted through the samplecell 102. As further illustrated in FIG. 1A, a third lens 120 may beinterposed between the sample cell 102 and the laser 108 and configuredto focus the beam of light 146 directed to and through the sample cell102.

In at least one implementation, at least one of the mirrors 126, 128 maybe associated with a respective detector 110, 112, and configured toreflect or redirect the light (e.g., scattered light or analytescattered light) towards the respective detector 110, 112. For example,as illustrated in FIG. 1A, a first mirror 126 may be disposed proximalthe first lens 116 and configured to reflect at least a portion of thelight from the first lens 116 towards a first detector 110. In anotherexample, a second mirror 128 may be disposed proximal the second lens118 and/or interposed between the second and third lenses 118, 120, andconfigured to reflect at least a portion of the light from the secondlens 118 towards a second detector 112. In at least one implementation,one or more lenses 122, 124 may be interposed between the first andsecond mirrors 126, 128 and the first and second detectors 110, 112 tofocus, refract, or otherwise direct the light from the mirrors 126, 128to the detectors 110, 112. For example, as illustrated in FIG. 1A, afourth lens 122 may be interposed between the first detector 110 and thefirst mirror 126, and a fifth lens 124 may be interposed between thesecond detector 112 and the second mirror 128.

In at least one implementation, at least one of the detectors 110, 112,114 may be configured to receive the light (e.g., scattered light oranalyte scattered light) from the sample cell 102 without the aid orreflection of one of the mirrors 126, 128. For example, as illustratedin FIGS. 1A and 1B, a third detector 114 may be disposed adjacent to orcoupled with the sample cell 102 and configured to receive the light(e.g., scattered light) from the sample cell 102 at an angle of about90° with respect to the beam of light 146. As further discussed herein,an optically transparent material or a sixth lens 186 may be configuredto refract or direct the scattered light toward the third detector 114.

As illustrated in FIG. 1A, at least one of the sample cell 102, thefirst, second, and third lenses 116, 118, 120, and the first and secondmirrors 126, 128 may be disposed parallel, coaxial, or otherwise alignedwith one another along a direction of the beam of light 146 emitted bythe laser 108. As further illustrated in FIG. 1A, each of the first andsecond detectors 110, 112 may be disposed or positioned to receive light(e.g., scattered light or analyte scattered light) from the respectivemirrors 126, 128 in a direction generally perpendicular to the beam oflight 146 emitted by the laser 108. Each of the first and second mirrors126, 128 may define a respective bore or pathway 150, 152 extendingtherethrough. For example, the first mirror 126 may define a bore 150extending therethrough in a direction parallel, coaxial, or otherwisealigned with the beam of light 146. Similarly, the second mirror 128 maydefine a bore 152 extending therethrough in the direction parallel,coaxial, or otherwise aligned with the beam of light 146. It should beappreciated that the bores 150, 152 extending through the respectivemirrors 126, 128 may allow the beam of light 146 emitted from the laser108 to be transmitted through the first and second mirrors 126, 128 tothereby prevent the beam of light 146 from being reflected towards thefirst and second detectors 110, 112.

FIG. 1D illustrates an enlarged view of the portion of the exemplary LSD100 indicated by the box labeled 1D of FIG. 1C, according to one or moreimplementations. As previously discussed, the body 130 of the samplecell 102 may at least partially define the channel or flowpath 144extending therethrough. For example, as illustrated in FIG. 1D, an innersurface 154 of the body 130 may at least partially define the flowpath144 extending therethrough. The flowpath 144 may define a volume of thesample cell 102. The flowpath 144 may include a central axis orcenterline 156 extending therethrough and configured to define a generalorientation of the flowpath 144. As illustrated in FIG. 1B, the flowpath144 and the central axis 156 thereof may be aligned or coaxial to thebeam of light 146 emitted from the laser 108. The flowpath 144 of thesample cell 102 may be interposed between the first and second lenses116, 118. In at least one implementation, the first and second lenses116, 118 may sealingly engage the body 130 of the sample cell 102 onopposing sides thereof to thereby prevent a flow of the sample oreffluent from the flowpath 144 via the interface between the body 130and the respective first and second lenses 116, 118. In anotherimplementation, a seal (e.g., gasket, O-ring, etc.) (not shown) may bedisposed between the body 130 and the first and second lenses 116, 118to provide a fluid tight seal therebetween.

The flowpath 144 may include an inner section 158 and two outer sections160, 162 disposed along the centerline 156 thereof. As illustrated inFIG. 1D, the inner section 158 may be interposed between the two outersections 160, 162. The inner section 158 may be fluidly coupled with andconfigured to receive a sample or effluent from the sample source 104.For example, as illustrated in FIG. 1D with continued referenced to FIG.1A, the body 130 of the sample cell 102 may define an inlet 164extending therethrough and configured to fluidly couple the samplesource 104 with the inner section 158 via line 106. In a preferredimplementation, the inlet 164 is configured such that the sample fromthe sample source 104 is directed to the middle or center of theflowpath 144 or the inner section 158 thereof.

In at least one implementation, the inner section 158 may be cylindricalor define a cylindrical volume, and may have a circular cross-sectionalprofile. It should be appreciated, however, that the cross-sectionalprofile may be represented by any suitable shape and/or size. Forexample, the cross-sectional profile may be elliptical, rectangular,such as a rounded rectangle, or the like. The inner section 158 may haveany suitable dimension. In at one implementation, the inner section 158may have a length extending between the two outer sections 160, 162 offrom about 4 mm to about 12 mm or greater. For example, the innersection 158 may have a length of from about 4 mm, about 5 mm, about 6mm, about 7 mm, or about 7.5 mm to about 8.5 mm, about 9 mm, about 10mm, about 11 mm, about 12 mm, or greater. In another example, the innersection 158 may have a length of from about 4 mm to about 12 mm, about 5mm to about 11 mm, about 6 mm to about 10 mm, about 7 mm to about 9 mm,or about 7.5 mm to about 8.5 mm. In a preferred implementation, theinner section 158 may have a length of from about 7 mm to about 9 mm,preferably about 7.5 mm to about 8.5 mm, more preferably about 8 mm. Inat least one implementation, the inner section 158 may have a diameterof from about 1.2 mm to about 2.0 mm or greater. For example, the innersection 158 may have a diameter of from about 1.2 mm, about 1.3 mm,about 1.4 mm, about 1.5 mm, or about 1.55 mm to about 1.65 mm, about 1.7mm, about 1.8 mm, about 1.9 mm, about 2.0 mm, or greater. In anotherexample, the inner section 158 may have a diameter of from about 1.2 mmto about 2.0 mm, about 1.3 mm to about 1.9 mm, about 1.4 mm to about 1.8mm, about 1.5 mm to about 1.7 mm, or about 1.55 mm to about 1.65 mm. Ina preferred implementation, the inner section 158 may have a diameter offrom about 1.5 mm to about 1.7 mm, preferably about 1.55 mm to about1.65 mm, more preferably about 1.6 mm.

The outer sections 160, 162 of the flowpath 144 may be fluidly coupledwith the inner section 158 and configured to receive the sample oreffluent therefrom. In at least one implementation, at least one of thefirst and second outer sections 160, 162 may be cylindrical or define acylindrical volume, and may have a circular cross-sectional profile. Forexample, at least one of the first and second outer sections 160, 162may be sized and shaped similar to the inner section 158 of FIG. 1D. Inanother implementation, at least one of the first and second outersections 160, 162 may be conical or frustoconical such that across-sectional area at a respective first end portion or inlet 166, 168thereof may be relatively less than a cross-sectional area at arespective second end portion or outlet 170, 172 thereof. In a preferredimplementation, the first and second outer sections 160, 162 may both befrustoconical or define a frustum, where the respective first endportions or inlets 166, 168 are configured to receive the sample fromthe inner section 158, and the respective second end portions or outlets170, 172 are configured to deliver the sample to a waste line 174 (seeFIG. 1A).

The inner surface 154 of the body 130 may at least partially definerespective taper angles (θ₁, θ₂) of the first outer section 160 and thesecond outer section 162. For example, as illustrated in FIG. 1D, theportion of the inner surface 154 defining or forming the first outersection 160 of the flowpath 144 and the centerline 156 of the flowpath144 may define the respective taper angle (θ₁) of the first outersection 160. In another example, the portion of the inner surface 154defining or forming the second outer section 162 of the flowpath 144 andthe centerline 156 of the flowpath 144 may define the respective taperangle (θ₂) of the second outer section 162. The first and second outersections 160, 162 may have any taper angles (θ₁, θ₂) capable of orconfigured to allow the LSD 100 and the detectors 110, 112, 114 thereofto receive scattered light at any desired angle. While FIG. 1Dillustrates the taper angles (θ₁, θ₂) of the first and second outersections 160, 162 to be relatively equal to one another, it should beappreciated that one of the taper angles (θ₁, θ₂) may be relativelygreater than the other. It should further be appreciated that than anyone or more attributes (e.g., length, taper angle, diameter, shape,size, etc.) of the first and second outer sections 160, 162 may bedifferent. In a preferred implementation, the attributes (e.g., length,taper angle, diameter, shape, size, etc.) of the first outer section 160and the second outer section 162 are the same or substantially the same.

Each of the outer sections 160, 162 may be fluidly coupled with thewaste line 174. For example, as illustrated in FIGS. 1A and 1D, the body130 may define a first outlet 176 and a second outlet 178 extendingtherethrough and configured to fluidly couple the first outer section160 and the second outer section 162 with the waste line 174 via a firstoutlet line 180 and a second outlet line 182, respectively. As furtherillustrated in FIG. 1D, the first and second outlets 176, 178 may befluidly coupled with the respective second end portions 170, 172 of theouter sections 160, 162. It should be appreciated that the orientation(e.g., circumferential orientation) or location of the inlet 164 and thefirst and second outlets 176, 178 may vary. For example, the inlet 164may be circumferentially aligned with at least one of the first andsecond outlets 176, 178. In another example, the inlet 164 may becircumferentially offset from at least one of the first and secondoutlets 176, 178. In yet another example, the first and second outlets176, 178 may be circumferentially aligned with one another orcircumferentially offset from one another.

As illustrated in FIG. 1D, the body 130 of the sample cell 102 maydefine an aperture 184 extending through at least a portion thereof, andconfigured to allow light (e.g., scattered light) from the inner section158 to be directed or transmitted to the third detector 114. Theaperture 184 may be sealed with an optically transparent material 186,such as a quartz crystal, to thereby allow the light from the innersection 158 to be directed to the third detector 114. In an exemplaryimplementation, illustrated in FIGS. 1B and 1D, the opticallytransparent material 186 may be shaped to refract a portion of the lighttowards the third detector 114. For example, the optically transparentmaterial 186 may be the sixth lens (e.g., a ball lens) configured toseal the aperture 184 and at least partially refract the light towardsthe third detector 114.

The body 130 may include or be fabricated from any suitable material.The body 130 may be configured such that the inner surface 154 thereofattenuates the reflection of light. For example, the body 130 may befabricated from a non-reflective material. In another example, the body130 may be at least partially fabricated from a reflective material andat least partially coated with a non-reflective material. In at leastone implementation, the sample cell 102 may be fabricated from quartz,such as black quartz. In an exemplary implementation, the body 130 mayinclude or be fabricated from a polymer. Illustrative polymers may be orinclude, but are not limited to, polyolefin-based polymers, acryl-basedpolymers, polyurethane-based polymers, ether-based polymers,polyester-based polymers, polyamide-based polymers, formaldehyde-basedpolymers, silicon-based polymers, any copolymers thereof, or anycombination thereof. For example, the polymers may include, but are notlimited to, poly(ether ether ketone) (PEEK), TORLON®, polyamide-imides,polyethylene (PE), polyvinyl fluoride (PVF), polyvinyl chloride (PVC),polyvinylidene fluoride (PVDF), polyvinylidene chloride (PVDC),polychlorotrifluoroethylene (PCTFE), polytetrafluoroethylene (PTFE),polypropylene (PP), poly(l-butene), poly(4-methylpentene), polystyrene,polyvinyl pyridine, polybutadiene, polyisoprene, polychloroprene,styrene-acrylonitrile copolymer, acrylonitrile-butadiene-styreneterpolymer, ethylene-methacrylic acid copolymer, styrene-butadienerubber, tetrafluoroethylene copolymer, polyacrylate, polymethacrylate,polyacrylamide, polyvinyl acetate, polyvinyl alcohol, polyvinyl butyral,polyvinyl ether, polyvinylpyrrolidone, polyvinylcarbazole, polyurethane,polyacetal, polyethylene glycol, polypropylene glycol, epoxy resins,polyphenylene oxide, polyethylene terephthalate, polybutyleneterephthalate, polydihydroxymethylcyclohexyl terephthalate, celluloseesters, polycarbonate, polyamide, polyimide, any copolymers thereof, orany combination thereof. The polymers may be or include, but are notlimited to, elastomers or elastomeric materials, synthetic rubber, orthe like. Illustrative elastomeric materials and synthetic rubbers mayinclude, but are not limited to, VITON, nitrile, polybutadiene,acrylonitrile, polyisoprene, neoprene, butyl rubber, chloroprene,polysiloxane, styrene-butadiene rubber, hydrin rubber, silicone rubber,ethylene-propylene-diene terpolymers, any copolymers thereof, or anycombination thereof.

In an exemplary operation of the LSD 100, with continued reference toFIGS. 1A-1D, the sample source 104 (e.g., a liquid chromatographincluding a gel permeation chromatography column) may inject or directthe sample or effluent (e.g., dilute particle and/or polymer solution)to and through the flowpath 144 of the sample cell 102 via line 106 andthe inlet 164. As illustrated in FIG. 1D, the sample from the samplesource 104 may be directed toward a center or middle of the flowpath 144and/or the inner section 158 of the sample cell 102. As the sample flowsto the center of the inner section 158, the flow of the of sample maysplit such that a first portion of the sample flows towards the firstouter section 160, and a second portion of the sample flows towards thesecond outer section 162. The portions of the sample in the first andsecond outer sections 160, 162 may then be directed out of the samplecell 102 and to the waste line 174 via the first and second outlets 176,178 and the first and second outlet lines 180, 182, respectively.

The rate of flow of the sample through the first outer section 160 andthe second outer section 162 may be modified or adjusted (i.e.,increased or decreased) by adjusting the respective lengths of the firstoutlet line 180 and the second outlet line 182. In at least oneimplementation, a rate of flow of the first and second portions of thesample through the first and second outer sections 160, 162 may be thesame or substantially the same. For example, the rate of flow of thefirst portion of the sample through the first outer section 160 is thesame or substantially the same as the rate of flow of the second portionof the sample through the second outer section 162. In anotherimplementation, the rate of flow of the first and second portions of thesample through the first and second outer sections 160, 162 may bedifferent. It should be appreciated, however, that a time correction maybe applied if the rate of flow is different through the first and secondouter sections 160, 162.

As the sample flows through the flowpath 144 of the sample cell 102, thelaser 108 may emit the beam of light 146 along and through thecenterline 156 of the flowpath 144 via the bore 152 of the second mirror128. In at least one implementation, illustrated in FIG. 1A, the beam oflight 146 may be transmitted through the third lens 120, which may atleast partially focus the beam of light 146 along the centerline 156 ofthe flowpath 144. In another implementation, the third lens 120 may beomitted. In at least one implementation, an optional screen or diaphragm188 may be disposed between the laser 108 and the sample cell 102, andconfigured to “cleanup,” segregate, or otherwise filter stray light(e.g., halo of light) from the beam of light 146. For example, thediaphragm 188 may define a hole or aperture (e.g., adjustableaperture/iris) capable of or configured to filter out stray light fromthe beam of light 146.

At least a portion of the beam of light 146 may travel or be transmittedfrom the laser 108 to and through the sample cell 102, the first lens116, the bore 152 of the second mirror 128, and/or an optional diaphragm196. For example, at least a portion of the beam of light 146 may betransmitted unhindered or without interacting with any of the analytesin the sample from the laser 108 to and through the sample cell 102, thefirst lens 116, the bore 152 of the second mirror 128, and/or theoptional diaphragm 188. The remaining portion of the beam of light 146transmitted through the flowpath 144 may interact or otherwise contactanalytes suspended, dispersed, or otherwise disposed in the sampleand/or flowing through the sample cell 102.

The contact between the beam of light 146 and the analytes in the samplemay generate or induce scattered light or analyte scattered beams 190,192, 194 (see FIGS. 1A and 1B). For example, contact between the beam oflight 146 and the analytes contained in the sample or flowing throughthe flowpath 144 of the sample cell 102 may generate forward and backanalyte scattered beams 190, 192. In another example, contact betweenthe beam of light 146 and the analytes contained in the sample orflowing through the flowpath 144 of the sample cell 102 may generateright angle (e.g., about 90° relative to the centerline 156) scatteredbeams 194 in a direction generally perpendicular to the beam of light146.

It should be appreciated that the flow of the sample to the center ofthe flowpath 144 via the inlet 164 allows the sample to interactimmediately with the beam of light 146, thereby minimizing peakbroadening. For example, flowing the sample directly to the center ofthe flowpath 144 allows the sample to interact with the beam of light146 without flowing through at least half the length or volume of thesample cell 102 (e.g., in a lateral or axial direction) and the flowpath144 thereof. Flowing the sample directly to the center of the flowpath144 also minimizes the amount of time necessary for the sample tointeract with the beam of light 146 and generate the analyte scatteredbeams 190, 192, 194. It should further be appreciated that one or morecomponents of the LSD 100 are configured such that only light scatteredfrom the center of the flowpath 144 are collected by the detectors 110,112, 114. For example, at least one of the first lens 116, the firstmirror, and the fourth lens 122 may be configured to segregate forwardlight scattering 190 that originates from the center of the flowpath 144from forward light scattering 190 that originates from other regions ofthe flowpath 144, such that the first detector 110 only receives forwardlight scattering 190 that originates from the center of the flowpath144. Similarly, at least one of the second lens 116, the second mirror128, and the fifth lens 124 may be configured to segregate back lightscattering 192 that originates from the center of the flowpath 144 fromback light scattering 192 that originates from other regions of theflowpath 144, such that the second detector 112 only receives back lightscattering 192 that originates from the center of the flowpath 144.

As illustrated in FIG. 1A, the forward analyte scattered beams orforward scattered light 190 may be directed towards the first detector110 via the first lens 116, the first mirror 126, and the fourth lens122. At least a portion of the forward scattered light 190 may be atleast partially refracted by the convex surface defined along the firstend portion 136 of the first lens 116. As illustrated in FIG. 1A, theforward scattered light 190 may be refracted by the convex surfacetoward the first mirror 126, and the first mirror 126 may reflect theforward scattered light 190 toward the first detector 110 via the fourthlens 122. The fourth lens 122 may collect the forward scattered light190, and direct and/or focus the forward scattered light 190 toward thefirst detector 110.

The forward scattered light 190 may be scattered at varying angles offrom greater than 0° to less than 90°, relative to the beam of light 146emitted from the laser 108 and/or the centerline 156 of the flowpath144. For example, the forward scattered light 190 may be scattered atany angle of from greater than 0°, about 5°, about 10°, about 15°, about20°, about 25°, about 30°, about 35°, about 40°, or about 45° to about50°, about 55°, about 60°, about 65°, about 70°, about 75°, about 80°,about 85°, or less than 90°. In another example, the forward scatteredlight 190 may be scattered at any angle of from about 5°, about 6°,about 7°, about 8°, about 9°, or about 9.5° to about 10.5°, about 11°,about 12°, about 13°, about 14°, or about 15°, relative to the beam oflight 146 emitted from the laser 108 and/or the centerline 156 of theflowpath 144. In yet another example, the forward scattered light 190may be scattered at an angle of from about 5° to about 15°, about 6° toabout 14°, about 7° to about 13°, about 8° to about 12°, about 9° toabout 11°, or about 9.5° to about 10.5°. It should be appreciated thatthe LSD 100 and any component thereof may be configured to receive theforward scattered light 190 scattered at any angle greater than 0° andless than 90°. For example, any one or more attributes (e.g., shape,location, orientation, etc.) of the first detector 110, the first lens116, the first mirror 126, the fourth lens 122, and/or any additionaloptional diaphragms may be adjusted, modified, or otherwise configuredsuch that the first detector 110 may receive any of the forwardscattered light 190. In a preferred implementation, the LSD 100 and thefirst detector 110 thereof is configured to receive or collect theforward scattered light 190 at an angle of from about 9° to about 11°,preferably about 9.5° to about 10.5°, and more preferably at an angle ofabout 10°, relative to the beam of light 146 and/or the centerline 156of the flowpath 144.

As illustrated in FIG. 1A, the back analyte scattered beams or backscattered light 192 may be directed towards the second detector 112 viathe second lens 118, the second mirror 128, and the fifth lens 124. Atleast a portion of the back scattered light 192 may be at leastpartially refracted by the convex surface of the second lens 118. Asillustrated in FIG. 1A, the back scattered light 192 may be refracted bythe convex surface toward the second mirror 128, and the second mirror128 may reflect the back scattered light 192 toward the second detector112 via the fifth lens 124. The fifth lens 124 may collect the backscattered light 192, and direct and/or focus the back scattered light192 toward the second detector 112.

The back scattered light 192 may be scattered at varying angles of fromgreater than 90° to less than 180°, relative to the beam of light 146emitted from the laser 108 and/or the centerline 156 of the flowpath144. For example, the back scattered light 192 may be scattered at anyangle of from greater than 90°, about 95°, about 100°, about 105°, about110°, about 115°, about 120°, about 125°, about 130°, or about 135° toabout 140°, about 145°, about 150°, about 155°, about 160°, about 165°,about 170°, about 175°, or less than 180°. In another example, the backscattered light 192 may be scattered at any angle of from about 165°,about 166°, about 167°, about 168°, about 169°, or about 169.5° to about170.5°, about 171°, about 172°, about 173°, about 174°, or about 175°,relative to the beam of light 146 emitted from the laser 108 and/or thecenterline 156 of the flowpath 144. In yet another example, the backscattered light 192 may be scattered at an angle of from about 165° toabout 175°, about 166° to about 174°, about 167° to about 173°, about168° to about 172°, about 169° to about 171°, or about 169.5° to about170.5°. It should be appreciated that the LSD 100 and any componentthereof may be configured to receive the back scattered light 192scattered at any angle greater than 90° and less than 180°. For example,any one or more attributes (e.g., shape, location, orientation, etc.) ofthe second detector 112, the second lens 118, the second mirror 128, thefifth lens 124, and/or any additional optional diaphragms may beadjusted, modified, or otherwise configured such that the seconddetector 112 may receive any of the back scattered light 192. In apreferred implementation, the LSD 100 and the second detector 112thereof is configured to receive or collect the back scattered light 192at an angle of from about 169° to about 171°, preferably about 169.5° toabout 170.5°, and more preferably at an angle of about 170°, relative tothe beam of light 146 and/or the centerline 156 of the flowpath 144.

As illustrated in FIG. 1D, the right angle analyte scattered beams orright angle scattered light 194 may be directed towards the thirddetector 114 via the aperture 184 extending between the third detector114 and the inner section 158 of the flowpath 144. In at least oneimplementation, the third detector 114 may be disposed in the aperture184 adjacent the inner section 158. In another implementation,illustrated in FIG. 1D, the optically transparent material 186 may bedisposed in the aperture 184 to seal the inner section 158 of theflowpath 144. The optically transparent material 186 may be any suitablematerial capable of allowing the right angle scattered light 194 to betransmitted to the third detector 114. The optically transparentmaterial 186 may be shaped to refract at least a portion of the rightangle scattered light 194 toward the third detector 114. For example, aspreviously discussed, the optically transparent material 186 may be aball lens shaped to refract the right angle scattered light 194 towardthe third detector 114.

The right angle scattered light 194 may be scattered in a directiongenerally perpendicular to the beam of light 146 and/or the centerline156 of the flowpath 144. For example, the right angle scattered light194 may be scattered at an angle of from about 87°, about 88°, about89°, about 89.5°, or about 90° to about 90.5°, about 91°, about 92°, orabout 93°. In another example, the right angle scattered light 194 maybe scattered at an angle of from about 87° to about 93°, about 88° toabout 92°, about 89° to about 91°, or about 89.5° to about 90.5°. Itshould be appreciated that the LSD 100 and any component thereof may beconfigured to receive the right angle scattered light 194 scattered in adirection generally perpendicular to the beam of light 146 and/or thecenterline 156 of the flowpath 144. For example, the shape, location,orientation, or any other attributes of the optically transparentmaterial 186 (e.g., the sixth lens) and/or the third detector 114 may beadjusted, modified, or otherwise configured such that the third detector114 may receive any of the right angle scattered light 194. In apreferred implementation, the LSD 100 and the third detector 114 thereofis configured to receive or collect the right angle scattered light 194at an angle of from about 89° to about 91°, preferably about 89.5° toabout 90.5°, and more preferably at an angle of about 90°, relative tothe beam of light 146 and/or the centerline 156 of the flowpath 144.

The present disclosure may provide methods for determining a radius ofgyration (Rg) of a particle (e.g., nanoparticle, microparticle, etc.) insolution using a light scattering detector, such as the LSD 100disclosed herein. The particle may be, for example, a polymer, aprotein, a protein conjugate, or a DNA fragment. For example, thepresent disclosure may provide methods for determining the radius ofgyration (Rg) of a particle in solution by analyzing data (e.g., via anelectronic processor or computer system) from the light scatteringdetector (e.g., the LSD 100). While reference may be made to the LSD 100and the components thereof described herein, it should be appreciatedthat the methods for determining the radius of gyration (Rg) may beconducted or performed with any suitable light scattering detector.

The method for determining a radius of gyration (Rg) of a particle insolution using a light scattering detector (e.g., the LSD 100) mayinclude passing or flowing the particle in solution through a flowpath144 in a sample cell 102 of the LSD 100, where the centerline 156 of theflowpath 144 is aligned with the beam of light 146 of the LSD 100. Themethod may also include normalizing one or more angles of the lightscattering detector (e.g., the LSD 100) or determining an angularnormalization factor (N_(θ)) for the one or more angles of the lightscattering detector. For example, the method may include determining anangular normalization factor (N_(θ)) for a first angle. In anotherexample, the method may include determining an angular normalizationfactor (N_(θ)) for a first angle and a second angle. As furtherdiscussed herein, the first angle may be either about 90° or about 170°relative to the centerline 156 of the flowpath 144, and the second anglemay be either about 90° or about 170° and different from the firstangle. The method may also include obtaining a first scatteringintensity (I_(θ1)) of the particle in solution at the first angle. Themethod may also include optionally obtaining a second light scatteringintensity (I_(θ2)) of the particle in solution at the second angle. Themethod may further include obtaining a 10° scattering intensity (I₁₀) ofthe particle in solution at an angle of about 10° or less. The methodmay also include determining a first particle scattering factor (P_(θ1))with the first scattering intensity (I_(θ1)), the 10° scatteringintensity (I₁₀), and the angular normalization factor (N_(θ1)) for thefirst angle. The method may also include optionally determining a secondparticle scattering factor (P_(θ2)) with the second scattering intensity(I_(θ2)), the 10° scattering intensity (I₁₀), and the angularnormalization factor (N_(θ2)) for the second angle. The method may alsoinclude plotting an angular dissymmetry plot, fitting a line to theangular dissymmetry plot, and determining a slope of the line of theangular dissymmetry plot at a selected location. The method may alsoinclude determining the radius of gyration (Rg) of the particle insolution from the slope of the line, and optionally, outputting ordisplaying the radius of gyration.

As discussed above, the method for determining the radius of gyration(Rg) of the particle in solution may include normalizing the one or moreangles of the light scattering detector or determining an angularnormalization factor (N_(θ)) for the one or more angles of the LSD 100.Determining an angular normalization factor (N_(θ)) for one or moreangles of the LSD 100 may be performed to account for scattering volumedifferences of the LSD 100 or varying sensitivities of any one or moreof the detectors 110, 112, 114.

In at least one implementation, only one angle of the LSD 100 isnormalized. For example, one or a first angle of the LSD 100 that may benormalized may include either an angle of about 90° or about 170°. Inanother implementation, two or first and second angles of the LSD 100are normalized. For example, a first angle at about 90° and a secondangle at about 170° are normalized. The number of angles normalized maybe at least partially determined by a size or radius of gyration of theparticle. For example, only one or the first angle of the LSD 100 may benormalized for determining the Rg of a particle having an Rg of lessthan or equal to about 10 nm. In another example, two or first andsecond angles of the LSD 100 may be normalized for determining the Rg ofa particle having an Rg of about 10 nm or greater to about 100 nm. Itshould be appreciated that the first and second angles of the LSD 100may also be normalized for determining the Rg of a particle having an Rgof less than 10 nm.

Normalizing an angle (e.g., 90°, 170°, etc.) of the LSD 100 ordetermining an angular normalization factor (N_(θ)) for the angle mayinclude passing a plurality of known particle standards (e.g., knownpolymer standards) in solution through the flowpath 144 of the samplecell 102, passing the beam of light 146 through the centerline 156 ofthe flowpath 144, collecting the analyte scattered light 192, 194 at theangle, and determining a scattering intensity (I_(θ)) at the angle withthe analyte scattered light 192, 194 collected at the angle. Forexample, determining the angular normalization factor (N_(θ)) for anangle of about 90° or about 170° may include passing a plurality ofknown particle standards in solution through the flowpath 144 of thesample cell 102, passing the beam of light 146 through the centerline156 of the flowpath 144, collecting the analyte scattered light 192, 194at the angle of about 90° or about 170°, respectively, and determining ascattering intensity (I_(θ)) at the angle of about 90° (I₉₀) or about170° (I₁₇₀) with the analyte scattered light 192, 194 collected at theangle of about 90° or about 170°, respectively.

Determining the angular normalization factor (N_(θ)) for the angle(e.g., 90°, 170°, etc.) may also include collecting the analytescattered light 190 at an angle (e.g., 0°) close to or incident with thebeam of light 146 and determining a scattering intensity (I₀) at theangle close to or incident with the beam of light. It should beappreciated that collecting the analyte scattered light 190 at an angleof about 0° relative to the centerline 156 is not possible, as thesignal from the beam of light 146 is relatively greater than any analytescattered light at the angle of about 0°; and thus, would mask anyanalyte scattered light at the angle of about 0°. As such, the analytescattered light 190 is collected at an angle close to the beam of light146. For example, it is assumed that analyte scattered light 190collected at an angle of about 10° or less is equivalent to the analytescattered light collected at about 0°. As such, the scattering intensityat an angle of about 10° (I₁₀) is equivalent or substantially equivalentto the scattering intensity at about 0° (I₀).

Determining the angular normalization factor (N_(θ)) for the angle(e.g., 90°, 170°, etc.) may also include plotting a ratio of thescattering intensity values of each of the plurality of known particlesat the angle (e.g., 90°, 170°, etc.) to the scattering intensity valuesof each of the plurality of known particles at an angle of about 10°(I₁₀), namely a ratio of (I_(θ)/I₁₀), versus a respective weight averagemolecular weight of each of the plurality of known particles. Anillustrative plot of the ratio (I_(θ)/I₁₀) versus the respective weightaverage molecular weight of each of the plurality of known particles isshown in FIG. 2. For example, determining the angular normalizationfactor (N₉₀) for an angle of about 90° may include plotting the ratio(I₉₀/I₁₀) of the scattering intensity (I₉₀) values of each of theplurality of known particles at an angle of about 90° to the scatteringintensity values (I₁₀) of each of the plurality of known particles at anangle of about 10° versus the respective weight average molecular weightof each of the plurality of known particles. In another example,determining the angular normalization factor (N₁₇₀) for an angle ofabout 170° may include plotting the ratio (I₁₇₀/I₁₀) of the scatteringintensity (I₁₇₀) values of each of the plurality of known particles atan angle of about 170° to the scattering intensity (I₁₀) values of eachof the plurality of known particles at an angle of about 10° versus therespective weight average molecular weight of each of the plurality ofknown particles.

Determining the angular normalization factor (N_(θ)) for the angle(e.g., 90°, 170°, etc.) may also include fitting a line to the plot ofthe ratio (I_(θ)/I₁₀) versus the respective weight average molecularweight of each of the plurality of known particles. For example, asillustrated in FIG. 2, determining the angular normalization factor(N₉₀) for the angle at about 90° may include fitting a line 202 to theplot of the ratio (I₉₀/I₁₀) versus the respective weight averagemolecular weight of each of the plurality of known particles. In anotherexample, illustrated in FIG. 2, determining the angular normalizationfactor (N₁₇₀) for the angle at about 170° may include fitting a line 204to the plot of the ratio (I₁₇₀/I₁₀) versus the respective weight averagemolecular weight of each of the plurality of known particles.

Determining the angular normalization factor (N_(θ)) for the angle(e.g., 90°, 170°, etc.) may further include extrapolating the respectivelines 202, 204 of each of the plots to determine the angularnormalization factor (N_(θ)). It should be appreciated that the angularnormalization factor (N_(θ)) for the angle may be the extrapolated valueat a molecular weight or x-value of 0. For example, the angularnormalization factor (N_(θ)) for the respective angle may be the valueat a respective y-intercept 206, 208 of each of the lines 202, 204. Forexample, as illustrated in FIG. 2, the angular normalization factor(N₉₀), as determined by the y-intercept 206, for the angle at about 90°is about 1.0099. As further illustrated in FIG. 2, the angularnormalization factor (N₁₇₀), as determined by the y-intercept 208, forthe angle at about 170° is about 0.7807.

As discussed above, the method for determining the radius of gyration(Rg) of the particle in solution may include obtaining a first lightscattering intensity (I_(θ1)) of the particle in solution (e.g., theunknown particle in solution) at the first angle (e.g., 90°, 170°,etc.), and optionally obtaining a second light scattering intensity(I_(θ2)) of the particle in solution at the second angle. For example,the method may include passing the particle in solution through theflowpath 144 in the sample cell 102, collecting the analyte scatteredlight 192, 194 at the first angle and/or the second angle, anddetermining the scattering intensity of the first angle (I_(θ1)) and/orthe second angle (I_(θ2)).

The method may also include obtaining a scattering intensity (I₀) of theparticle in solution at an angle close to or incident with the beam oflight 146 by collecting the analyte scattered light 190 at an angle ofabout 0° relative to the centerline 156. As discussed above, collectingthe analyte scattered light 190 at an angle of about 0° relative to thecenterline 156 is not possible, as the signal from the beam of light 146is relatively greater than any analyte scattered light at the angle ofabout 0°; and thus, would mask any analyte scattered light at the angleof about 0°. As such, the analyte scattered light 190 of the particle insolution is collected at an angle close to the beam of light 146. Forexample, it is assumed that analyte scattered light 190 collected at anangle of about 10° or less is equivalent to the analyte scattered lightcollected at about 0°. As such, the scattering intensity (I₁₀) of theparticle in solution at an angle of about 10° is equivalent to thescattering intensity (I₀) of the particle in solution at about 0°.

As discussed above, the method for determining the radius of gyration(Rg) of the particle in solution may include determining a firstparticle scattering factor (P_(θ1)) with or utilizing the firstscattering intensity (I_(θ1)), the 10° scattering intensity (I₁₀), andthe angular normalization factor (N_(θ1)) for the first angle. Themethod for determining the radius of gyration (Rg) of the particle insolution may also, optionally, include determining a second particlescattering factor (P_(θ2)) with or utilizing the second scatteringintensity (I_(θ2)), the 10° scattering intensity (I₁₀), and the angularnormalization factor (N_(θ2)) for the second angle.

In at least one implementation, the particle scattering factor (P_(θ))may be represented by equation (1):

$\begin{matrix}{{P_{\theta \;} = \frac{\left( {I_{\theta \;}/I_{10}} \right)}{N_{\theta}}},} & (1)\end{matrix}$

where:

-   -   I_(θ) may be the scattering intensity of the particle in        solution at a respective angle (e.g., about 90° or about 170°);    -   I₁₀ is the scattering intensity of the particle in solution at        an angle of about 10° or less; and    -   N_(θ) is the angular normalization factor for the respective        angle.        It should be appreciated that the particle scattering factor        (P₀) at 0° may be assumed to be the same particle scattering        factor (P₁₀) at about 10°, which is equal to one (1).

As discussed above, the method for determining the radius of gyration(Rg) of the particle in solution may further include plotting an angulardissymmetry plot. Illustrative angular dissymmetry plots are shown inFIGS. 3 and 4. The angular dissymmetry plot may include one or morepoints on a plane. For example, the angular dissymmetry plot may includeone, two, three, four, or more points on a plane. As illustrated in FIG.3, the angular dissymmetry plot may include a first point 302 and asecond point 304. As further illustrated in FIG. 4, the angulardissymmetry plot may include a first point 402, a second point 404, anda third point 406. Each of the points 302, 304, 402, 404, 406 mayinclude a first coordinate, such as an x-coordinate, and a secondcoordinate, such as a y-coordinate. The first or x-coordinate may berepresented by μ², which may be expressed by equation (2):

$\begin{matrix}{{\mu_{\theta}^{2} = \left( \frac{4\pi \; n_{0}\sin \frac{\theta}{2}}{\lambda} \right)^{2}},} & (2)\end{matrix}$

where:

-   -   n₀ is a refractive index of the solution in which the particle        is contained;    -   θ is the respective angle (e.g., about 90° or about 170°); and    -   λ is a wavelength of the beam of light.        The second or y-coordinate may be represented by the respective        particle scattering factor (P_(θ)). It should be appreciated        that the beam of light may have any suitable wavelength. In at        least one implementation, the wavelength may be from about 400        nm to about 600 nm. For example, the wavelength of the beam of        light may be from about 400 nm, about 450 nm, or about 500 nm to        about 550 nm, or about 600 nm. In a preferred implementation,        the wavelength of the beam of light may be from about 450 nm to        about 550 nm, about 500 nm to about 530 nm, or about 515 nm. In        one implementation, the wavelength of the beam of light may        exclude wavelengths of about 600 nm or greater to about 700 nm.

As illustrated in FIG. 3, the angular dissymmetry plot may include thefirst point 302 corresponding to the angle at 0°, or about 10° based onthe assumption discussed above, and the second point 304 correspondingto either an angle of about 90° or an angle of about 170°. A first orx-coordinate of the first point 302 is equal to μ², which according toequation 2 is equal to zero (0). A second coordinate of the first point302 is equal to the particle scattering factor (P₁₀), which is equal toone (1). Similarly, a first or x-coordinate of the second point 304 isequal to μ² calculated at either about 90° or about 170°, and a secondor y-coordinate of the second point 304 is equal to the respectiveparticle scattering factor (P₀). As illustrated in FIG. 4, the angulardissymmetry plot may include the first point 402 corresponding to theangle at 0°, or about 10° based on the assumptions discussed above, thesecond point 404 corresponding to the angle at about 90°, and the thirdpoint 406 corresponding to the angle at about 170°. The respective firstand second coordinates of each of the first, second, and third points402, 404, 406 of the angular dissymmetry plot of FIG. 4 may bedetermined as discussed above.

As discussed above, the method for determining the radius of gyration(Rg) of the particle in solution may also include fitting a line 306,408 to the angular dissymmetry plot. Fitting the line 306, 408 to theangular dissymmetry plot may include a least squares fitting. The line306, 408 may include a polynomial degree of less than three. The line306, 408 may be a straight line or a curved line. For example, asillustrated in FIG. 3, the line 306 may be a straight line and have apolynomial degree of one. In another example, illustrated in FIG. 4, theline 408 may be curved line that may have a quadratic relationship and apolynomial degree of two.

As discussed above, the method for determining the radius of gyration(Rg) of the particle in solution may include determining a slope of theline 306, 408 at a selected location on the line 306, 408. The selectedlocation on the line 306, 408 may be anywhere along the line. In atleast one implementation, the selected location on the line 306, 408 maybe at a y-intercept or where the x-value is zero.

The method for determining the radius of gyration (Rg) of the particlein solution may also include calculating or determining the radius ofgyration (Rg) of the particle in solution with or from the slope of theline 306, 408 at the selected location. The radius of gyration (Rg) ofthe particle in solution may be represented by equation (3):

Rg²=−3×b  (3),

where b is slope of the line at the selected location.

The method for determining the radius of gyration (Rg) of the particlein solution may also include outputting or displaying the radius ofgyration (Rg). For example, the method may include outputting the radiusof gyration (Rg) on a display (e.g., computer display), a readout, areport, or a disk storage of a computing system, such as the computingsystem described herein.

FIG. 5 illustrates a computer system or electronic processor 500 forreceiving and/or analyzing data from the LSD 100, according to one ormore implementations. The computer system or electronic processor 500may be a general purpose computer, and may allow a user orchromatographer to process data, analyze data, interpret data, storedata, retrieve data, display data, display results, interpret results,store results, or any combination thereof. The results may be graphicalin form and/or tabular in form. It should be appreciated that, while theelectronic processor 500 is shown operably and/or communicably coupledwith the LSD 100 of FIG. 1A, the electronic processor 500 may beoperably and/or communicably coupled with any suitable light scatteringdetector known in the art.

The computer system or electronic processor 500 may be capable of orconfigured to operate, communicate with (e.g., send/receive data),modify, modulate, or otherwise run any one or more components of the LSD100. For example, the electronic processor 500 may be operably and/orcommunicably coupled with and capable of or configured to operate,communicate with, modify, modulate, or otherwise run a pump (not shown),the laser 108, the sample source 104, any one or more of the detectors110, 112, 114, or any other component of the LSD 100.

In at least one implementation, illustrated in FIG. 5, the electronicprocessor 500 may be operably and/or communicably coupled with thedetectors 110, 112, 114 and capable of or configured to send and/orreceived signals and/or data 502 therefrom. The data 502 from the one ormore detectors 110, 112, 114 may be or include analog data, such asfluctuating analog voltage. In at least one implementation, theelectronic processor 500 may be capable of or configured to convert theanalog data to digital data. For example, the electronic processor 500may include an analog to digital converter (not shown). In anotherimplementation, an analog to digital converter may be interposed betweenthe LSD 100 or the detectors 110, 112, 114 thereof and the electronicprocessor 500.

The electronic processor 500 may be capable of or configured to receive,collect, record, and/or store data 502 from any one or more componentsof the LSD 100. For example, as illustrated in FIG. 5, the electronicprocessor 500 may receive data 502 from the one or more detectors 110,112, 114 of the LSD 100, optionally convert the data 502, and recordand/or store the data 502 in a computer memory, such as a local drive ornetwork drive (e.g., cloud drive).

The electronic processor 500 may be capable of or configured to analyze,process, display, and/or output data 502. For example, the electronicprocessor 500 may include software capable of or configured to analyze,process, display, and/or output data 502. The software may also becapable of or configured to process the data 502 and output or displaythe data 502 on a workstation or display 504. The software may includeany one or more of the algorithms, equations, methods, steps, processes,or formulas disclosed herein. The electronic processor 500 may processand/or extract information from the data 502 to prepare results, andpresent the data 502 and/or the results, such as in a report or on thedisplay 504. The electronic processor 500 may include a graphical userinterface (GUI) that allows a user or the chromatographer to interactwith all systems, subsystems, and/or components of the electronicprocessor 500 and/or the LSD 100.

FIG. 6 illustrates a block diagram of the computer system or electronicprocessor 500 of FIG. 5 that may be used in conjunction with one or morelight scattering detectors, including the LSD 100, and/or one or moremethods disclosed herein. For example, the computing system 500 (orsystem, or server, or computing device, or device) may represent any ofthe devices or systems described herein that perform any of theprocesses, operations, or methods of the disclosure. Note that while thecomputing system 500 illustrates various components, it is not intendedto represent any particular architecture or manner of interconnectingthe components as such details are not germane to the presentdisclosure. It will also be appreciated that other types of systems thathave fewer or more components than shown may also be used with thepresent disclosure.

As shown, the computing system 500 may include a bus 602 which may becoupled to a processor 604, ROM (Read Only Memory) 608, RAM (or volatilememory) 610, and storage (or non-volatile memory) 612. The processor 604may store data 502 (see FIG. 5) in one or more of the memories 608, 610,612. The processor 604 may also retrieve stored data from one or more ofthe memories 608, 610, and 612. The one or more memories 608, 610, 612may store the software disclosed therein, which may include instructionsto perform any one or more of the processes, operations, or methodsdescribed herein. The processor 604 may also retrieve stored software orthe instructions thereof from one or more of the memories 608, 610, and612 and execute the instructions to perform any one or more of theprocesses, operations, or methods described herein. These memoriesrepresent examples of a non-transitory computer-readable medium (ormachine-readable medium) or storage containing instructions which whenexecuted by a processor 604 (or system, or computing system), cause theprocessor 604 to perform any one or more of the processes, operations,or methods described herein. The RAM 610 may be implemented as, forexample, dynamic RAM (DRAM), or other types of memory that require powercontinually in order to refresh or maintain the data in the memory.Storage 612 may include, for example, magnetic, semiconductor, tape,optical, removable, non-removable, and/or other types of storage thatmaintain data even after power is removed from the computer system 500.It should be appreciated that storage 612 may be remote from the system500 (e.g. accessible via a network).

A display controller 614 may be coupled to the bus 602 in order toreceive data to be displayed on a display 504, which may display any oneof the user interface features or implementations described herein andmay be a local or a remote display device 504. The computing system 500may also include one or more input/output (I/O) components 616 includingmice, keyboards, touch screen, network interfaces, printers, speakers,and other devices. Typically, the input/output components 616 arecoupled to the system 500 through an input/output controller 618.

Modules 620 (or program code, instructions, components, subsystems,units, functions, or logic) may represent any of the instructions,subsystems, steps, methods, equations, calculations, plots, or enginesdescribed above. Modules 620 may reside, completely or at leastpartially, within the memories described above (e.g. non-transitorycomputer-readable media), or within a processor 604 during executionthereof by the computing system 500. In addition, Modules 620 may beimplemented as software, firmware, or functional circuitry within thecomputing system 500, or as combinations thereof.

The present disclosure has been described with reference to exemplaryimplementations. Although a limited number of implementations have beenshown and described, it will be appreciated by those skilled in the artthat changes may be made in these implementations without departing fromthe principles and spirit of the preceding detailed description. It isintended that the present disclosure be construed as including all suchmodifications and alterations insofar as they come within the scope ofthe appended claims or the equivalents thereof.

1. A method for determining a radius of gyration (Rg) of a particle insolution using a light scattering detector, the method comprising:passing the particle in solution through a flowpath in a sample cell,wherein the flowpath has a centerline aligned with a beam of light ofthe detector; determining an angular normalization factor (N_(θ1)) for afirst angle of the detector and an angular normalization factor (N_(θ2))of a second angle of the detector, wherein the first angle is about 90°relative to the centerline, and wherein the second angle is about 170°relative to the centerline; obtaining a first scattering intensity(I_(θ1)) of the particle in solution at the first angle; obtaining asecond scattering intensity (I_(θ2)) of the particle in solution at thesecond angle; obtaining a 10° scattering intensity (I₁₀) of the particlein solution at an angle of about 10°; determining a first particlescattering factor (P_(θ1)) with the first scattering intensity (I_(θ1)),the 10° scattering intensity (I₁₀), and the angular normalization factor(N_(θ1)) for the first angle; determining a second particle scatteringfactor (P_(θ2)) with the second scattering intensity (I_(θ2)), the 10°scattering intensity (I₁₀), and the angular normalization factor(N_(θ2)) for the second angle; plotting an angular dissymmetry plot,wherein the angular dissymmetry plot comprises the first particlescattering factor (P_(θ1)) and the second particle scattering factor(P_(θ2)); fitting a line to the angular dissymmetry plot; determining aslope of the line at a selected location on the line; determining theradius of gyration (Rg) of the particle in solution from the slope ofthe line; and outputting the radius of gyration (Rg).
 2. The method ofclaim 1, wherein determining the angular normalization factor of thefirst and second angles of the detector comprises: passing each of aplurality of known particles in solution through the flowpath of thesample cell; obtaining scattering intensity values for each of theplurality of known particles in solution at an angle of about 10°, atthe first angle, and at the second angle; determining the angularnormalization factor (N_(θ1)) for the first angle with a plot of a ratioof the scattering intensity values of each of the plurality of knownparticles at the first angle to the scattering intensity values of eachof the plurality of known particles at an angle of about 10°;determining the angular normalization factor (N_(θ2)) for the secondangle with a plot of a ratio of the scattering intensity values of eachof the plurality of known particles at the second angle to thescattering intensity values of each of the plurality of known particlesat an angle of about 10°.
 3. The method of claim 2, wherein each of theplurality of known particles in solution have a known molecular weight.4. The method of claim 1, wherein the first particle scattering factor(P_(θ1)) is in the form${P_{\theta_{1}} = \frac{\left( {I_{\theta_{1}}/I_{10}} \right)}{N_{\theta_{1}}}},$where: I_(θ1) is the scattering intensity of the particle in solution atthe first angle; I₁₀ is the scattering intensity of the particle insolution at an angle of about 10°; and N_(θ1) is the angularnormalization factor for the first angle.
 5. The method of claim 1,wherein the second particle scattering factor (P_(θ2)) is in the form${P_{\theta_{2}} = \frac{\left( {I_{\theta_{2}}/I_{10}} \right)}{N_{\theta_{2}}}},$wherein: I_(θ2) is the scattering intensity of the particle in solutionat the second angle; I₁₀ is the scattering intensity of the particle insolution at an angle of about 10°; and N_(θ2) is the angularnormalization factor for the second angle.
 6. The method of claim 1,wherein plotting the angular dissymmetry plot comprises: plotting afirst point on a plane, the first point comprising a first coordinateand a second coordinate, wherein the first coordinate of the first pointis the first particle scattering factor (P_(θ1)), and wherein the secondcoordinate of the first point is in the form${\mu_{\theta_{1}}^{2} = \left( \frac{4\pi \; n_{0}\sin \frac{\theta_{1}}{2}}{\lambda} \right)^{2}},$wherein: n₀ is a refractive index of the solution; θ₁ is the firstangle; and λ is a wavelength of the beam of light; plotting a secondpoint on the plane, the second point comprising a first coordinate and asecond coordinate, wherein the first coordinate of the second point isthe second particle scattering factor (P_(θ2)), and wherein the secondcoordinate of the second point is in the form${\mu_{\theta_{2}}^{2} = \left( \frac{4\pi \; n_{0}\sin \frac{\theta_{2}}{2}}{\lambda} \right)^{2}},$wherein: n₀ is a refractive index of the solution; θ₂ is the secondangle; and λ is the wavelength of the beam of light.
 7. The method ofclaim 1, wherein fitting the line to the angular dissymmetry plotcomprises a least squares fitting, and wherein the line comprises apolynomial degree of less than three.
 8. A method for determining aradius of gyration (Rg) of a particle in solution using a lightscattering detector, the method comprising: passing the particle insolution through a flowpath in a sample cell, wherein the flowpath has acenterline aligned with a beam of light of the detector; determining anangular normalization factor (N_(θ1)) for a first angle of the detector,wherein the first angle is either about 90° or about 170° relative tothe centerline; obtaining a first scattering intensity (I_(θ1)) of theparticle in solution at the first angle; obtaining a 10° scatteringintensity (I₁₀) of the particle in solution at an angle of about 10° orless; determining a first particle scattering factor (P_(θ1)) with thefirst scattering intensity (I_(θ1)), the 10° scattering intensity (I₁₀),and the angular normalization factor (N_(θ1)) for the first angle;plotting an angular dissymmetry plot, wherein the angular dissymmetryplot comprises the first particle scattering factor (P_(θ1)); fitting aline to the angular dissymmetry plot; determining a slope of the line ata selected location on the line; determining the radius of gyration (Rg)of the particle in solution from the slope of the line; and outputtingthe radius of gyration.
 9. The method of claim 8, wherein determiningthe angular normalization factor (N_(θ1)) for the first angle of thedetector comprises: passing each of a plurality of known particles insolution through the flowpath of the sample cell; obtaining scatteringintensity values of each of the plurality of known particles in solutionat an angle of about 10° and at the first angle; and determining theangular normalization factor (N_(θ1)) for the first angle with a plot ofa ratio of the scattering intensity values of each of the plurality ofknown particles at the first angle to the scattering intensity values ofeach of the plurality of known particles at an angle of about 10° withrespect to a respective weight average molecular weight of each of theplurality of known particles in solution.
 10. The method of claim 9,wherein each of the plurality of known particles in solution have aknown molecular weight.
 11. The method of claim 8, wherein the firstparticle scattering factor (P_(θ1)) is in the form${P_{\theta_{1}} = \frac{\left( {I_{\theta_{1}}/I_{10}} \right)}{N_{\theta_{1}}}},$where: I_(θ1) is the scattering intensity of the particle in solution atthe first angle; I₁₀ is the scattering intensity of the particle insolution at an angle of about 10°; and N_(θ1) is the angularnormalization factor for the first angle.
 12. The method of claim 8,wherein plotting the angular dissymmetry plot comprises: plotting afirst point on a plane, the first point comprising a first coordinateand a second coordinate, wherein the first coordinate of the first pointis the first particle scattering factor (P_(θ1)), and wherein the secondcoordinate of the first point is in the form${\mu_{\theta_{1}}^{2} = \left( \frac{4\pi \; n_{0}\sin \frac{\theta_{1}}{2}}{\lambda} \right)^{2}},$wherein: n₀ is a refractive index of the solution; θ₁ is the firstangle; and λ is a wavelength of the beam of light.
 13. The method ofclaim 8, wherein the line of the angular dissymmetry plot is a straightline.
 14. The method of claim 8, wherein the radius of gyration (Rg) ofthe particle in solution is less than 10 nm.
 15. The method of claim 8,further comprising: obtaining an angular normalization factor (N_(θ2))of a second angle of the detector, wherein the second angle is eitherabout 90° or about 170° relative to the centerline, and wherein thesecond angle is different from the first angle; obtaining a secondscattering intensity (I_(θ2)) of the particle in solution at the secondangle; and determining a second particle scattering factor (P_(θ2)) withthe second scattering intensity (I_(θ2)), the 10° scattering intensity(I₁₀), and the angular normalization factor (N_(θ2)) for the secondangle, wherein the angular dissymmetry plot further comprises the secondparticle scattering factor (P_(θ2)).
 16. The method of claim 15, whereindetermining the angular normalization factor of the second angle of thedetector comprises: obtaining scattering intensity values of each of theplurality of known particles in solution at the second angle; anddetermining the angular normalization factor (N_(θ2)) for the secondangle with a plot of a ratio of the scattering intensity values of eachof the plurality of known particles at the second angle to thescattering intensity values of each of the plurality of known particlesat an angle of about 10° with respect to a respective weight averagemolecular weight of each of the plurality of known particles insolution.
 17. The method of claim 16, wherein the second particlescattering factor (P_(θ2)) is in the form${P_{\theta_{2}} = \frac{\left( {I_{\theta_{2}}/I_{10}} \right)}{N_{\theta_{2}}}},$wherein: I_(θ2) is the scattering intensity of the particle in solutionat the second angle; I₁₀ is the scattering intensity of the particle insolution at an angle of about 10°; and N_(θ2) is the angularnormalization factor for the second angle.
 18. The method of claim 12,wherein plotting the angular dissymmetry plot further comprises:plotting a second point on the plane, the second point comprising afirst coordinate and a second coordinate, wherein the first coordinateof the second point is the second particle scattering factor (P_(θ2)),and wherein the second coordinate of the second point is in the form${\mu_{\theta_{2}}^{2} = \left( \frac{4\pi \; n_{0}\sin \frac{\theta_{2}}{2}}{\lambda} \right)^{2}},$wherein: n₀ is a refractive index of the solution; θ₂ is the secondangle; and λ is the wavelength of the beam of light.
 19. The method ofclaim 15, wherein the line of the angular dissymmetry plot is a curvedline.
 20. The method of claim 15, wherein the radius of gyration (Rg) ofthe particle in solution is less than 100 nm, optionally greater than 10nm.